Question

The perimeter of the triangle below is 72 units. Fine the length of side PR write your answer without variables.

Answer 1

In this problem, we have a triangle with sides:

• PR = 4x,,

,

• RQ = x + 3,

,

• QP = 5x - 1,

,

• and perimeter p = 72.

By definition, the perimeter is the sum of the length of the sides, so we have:

$\begin{gathered} p=PR+RQ+QP, \\ 72=(4x)+(x+3)+(5x-1)\text{.} \end{gathered}$

Solving for x the last equation, we find that:

$\begin{gathered} 72=10x+2, \\ 72-2=10x \\ 70=10x \\ x=\frac{70}{10}=7. \end{gathered}$

Replacing the value x = 7 in the equation of side PR, we have:

$PR=4\cdot7=28.$

Answer

PR = 28